A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation

Xuemin Xue and Xiangtuan Xiong
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Xuemin Xue: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Xiangtuan Xiong: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2021, vol. 9, issue 18, 1-11

Abstract: In this paper, the numerical analytic continuation problem is addressed and a fractional Tikhonov regularization method is proposed. The fractional Tikhonov regularization not only overcomes the difficulty of analyzing the ill-posedness of the continuation problem but also obtains a more accurate numerical result for the discontinuity of solution. This article mainly discusses the a posteriori parameter selection rules of the fractional Tikhonov regularization method, and an error estimate is given. Furthermore, numerical results show that the proposed method works effectively.

Keywords: numerical analytic continuation; fractional Tikhonov regularization method; ill-posedness; error estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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